Height difference correlation function

(λ) = <(z(x + λ) − z(x))^2>
The HDC is a measure of how strongly neighbouring points are related to each other. Assuming two points of the surface have the distance λ, their heights are z(x) and z(x+λ), respectively. This is quite easy to calculate since I have the data for the surface profile which I am trying to analyse.

The squares are averaged using the "<...>" average over all realizations of the rough surface. This confuses me and I am not sure exactly how to implement this averaging process. Should I sum the adjacent points(and divide by 2) or divide by the total number of points (eg 1000) to get an average, etc?

Has anyone come across such a function previously and be able to point me in the rigt direction?